Finite Group Databasebeta

← C2×#20286834 #28260803

Subgroups — C2×#20286834 #28260803

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811315C211yesmaximal, characteristic, complemented
2C2×#16811292C211yesmaximal, characteristic
3#20286834C2116yesmaximal, direct product factor
4C2×#16810986C211yesmaximal, characteristic, complemented
5C2×#16810942C211yesmaximal, characteristic, complemented
6C2×#16810946C211yesmaximal, characteristic, complemented
7C2×#16810928C211yesmaximal, characteristic, complemented
8C2×#16810871C211yesmaximal, characteristic, complemented
9C2×#16810849C211yesmaximal, characteristic, complemented
10C2×#16810821C211yesmaximal, characteristic, complemented
11C2×#16810784C211yesmaximal, characteristic, complemented
12C2×#16810730C211yesmaximal, characteristic, complemented
13C2×#16810697C211yesmaximal, characteristic, complemented
14C2×#16810624C211yesmaximal, characteristic, complemented
15C2×#16810618C211yesmaximal, characteristic, complemented
16C2×C53×#452C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811315—24no—
22#16811315C2218yescomplemented
23#16811292—24no—
24#16811292C2218yes—
25C2×#13133213—21no—
26C2×#13133213C2211yescharacteristic
27C2×#13133212—21no—
28C2×#13133208—21no—
29C2×#13133208C2211yescharacteristic
30C2×#13133201—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133191—21no—
33C2×#13133191C2211yescharacteristic
34C2×#13133188—21no—
35C2×#13133188C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×C4×C22⋊D53C2211yescharacteristic
40C2×#13133175C2211yescharacteristic
41C2×#13133173—21no—
42C22×C4⋊Dic53C2211yescharacteristic
43#16810986C2218yescomplemented
44#16810946C2218yescomplemented
45#16810942C2218yescomplemented
46#16810928C2218yescomplemented
47#16810871C2218yescomplemented
48#16810849C2218yescomplemented
49#16810821C2218yescomplemented
50#16810784C2218yescomplemented
51#16810730C2218yescomplemented
52#16810697C2218yescomplemented
53C2×#13133150C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810624C2218yescomplemented
58#16810618C2218yescomplemented
59C2×#13133141C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#452C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C22×D212—21no—
82C22×D212C2311yescharacteristic
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C22⋊D53D411yescharacteristic
88C23×Dic53—21no—
89C22×C4×D53—21no—
90C22×C4×D53C2311yescharacteristic
91C2×#11719924—42no—
92C2×#11719924C2314yes—
93C2×#11719917—42no—
94C2×#11719917C2314yes—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C2×C8×D53—42no—
98C2×C8×D53C2314yes—
99#13133213—22no—
100#13133213—28no—
101#13133213C2314yes—
102#13133212—28no—
103#13133208—28no—
104#13133208—22no—
105#13133208C2314yes—
106#13133201—28no—
107#13133193—22no—
108#13133193C2314yes—
109#13133191—28no—
110#13133191—22no—
111#13133191C2314yes—
112#13133188—28no—
113#13133188—22no—
114#13133188C2314yes—
115Q8×Dic53—22no—
116Q8×Dic53—22no—
117Q8×Dic53C2314yes—
118Q8×Dic53C2314yes—
119C4×C22⋊D53—28no—
120C4×C22⋊D53D414yes—
121C4×C22⋊D53C2314yes—
122#13133175—22no—
123#13133175C2314yes—
124#13133173—28no—
125C2×C4⋊Dic53—22no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2314yes—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53D411yescharacteristic
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921D411yescharacteristic
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133150C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133146C2314yes—
151#13133141C2314yes—
152#13133141C2314yes—
153#13133141C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133129C2314yes—
160#13133127C2314yes—
161C2×#41×C53—22no—
162C2×#41×C53—24no—
163C2×#41×C53—42no—
164C2×#41×C53C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53C2311yescharacteristic
171C2×Q16×C53—24no—
172C2×Q16×C53C2314yes—
173C2×SD16×C53—42no—
174C2×SD16×C53C2314yes—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yes—
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182#103×C53C2314yes—
183#102×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53C2×D411yescharacteristic
189#41×C53—28no—
190#41×C53—44no—
191#41×C53—48no—
192C2×Q8×C53—21no—
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53—22no—
197C2×Q8×C53#4114yes—
198C2×Q8×C53C2412yes—
199C2×Q8×C53C2412yes—
200C2×D4×C53—24no—
201C2×D4×C53—21no—
202C2×D4×C53—22no—
203C2×D4×C53—22no—
204C2×D4×C53—44no—
205C2×D4×C53C2412yes—
206C22×C4×C53—21no—
207C22×C4×C53—22no—
208C22×C4×C53—22no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—24no—
212C22×C4×C53—44no—
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D412yes—
215C22×C4×C53C2412yes—
216C22×C4×C53C2411yescharacteristic
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—42no—
222C2×C22⋊D53—44no—
223C2×C22⋊D53—82no—
224C2×C22⋊D53—82no—
225C2×C22⋊D53—82no—
226C2×C22⋊D53C2×D414yes—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—24no—
231C22×Dic53—44no—
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234C22×Dic53C2×D411yescharacteristic
235#11719949—28no—
236#11719949—44no—
237#11719949—48no—
238C2×D212—22no—
239C2×D212—22no—
240C2×D212—24no—
241C2×D212—21no—
242C2×D212—44no—
243C2×D212C2412yes—
244C2×C4×D53—22no—
245C2×C4×D53—22no—
246C2×C4×D53—24no—
247C2×C4×D53—44no—
248C2×C4×D53C2×D412yes—
249C2×C4×D53C2412yes—
250Q16×C53—28no—
251SD16×C53—44no—
252C2×C8×C53—22no—
253C2×C8×C53—22no—
254C2×C8×C53C2412yes—
255C2×C8×C53C2412yes—
256C4⋊C4×C53—24no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53C2412yes—
259C22⋊C4×C53—24no—
260C22⋊Dic53—24no—
261C22⋊Dic53C2×D414yes—
262#11719924—44no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921C2×D414yes—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
269C4⋊Dic53—24no—
270C4⋊Dic53—21no—
271C4⋊Dic53—24no—
272C4⋊Dic53—24no—
273C4⋊Dic53—24no—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276C4⋊Dic53C2412yes—
277#11719919—24no—
278#11719919—24no—
279#11719919C2×D414yes—
280C4×Dic53—24no—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53C2×D412yes—
284C4×Dic53C2412yes—
285#11719917—44no—
286C2×#88322—22no—
287C2×#88322—22no—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290C8×D53—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53C22×D412yes—
308Q8×C53—24no—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—22no—
312Q8×C53—42no—
313Q8×C53C2×#4114yes—
314D4×C53—22no—
315D4×C53—22no—
316D4×C53—48no—
317D4×C53—42no—
318C2×C4×C53—24no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—24no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—48no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D411yescharacteristic
331C2×C4×C53C2×#4112yes—
332C2×C4×C53H(5,𝔽2)12yes—
333C2×C4×C53C2511yescharacteristic
334C22⋊D53—44no—
335C22⋊D53—48no—
336C22⋊D53—84no—
337C22⋊D53—84no—
338C22⋊D53—84no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—48no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53C22×D412yes—
350C2×Dic53C22×D412yes—
351C2×Dic53C22×D412yes—
352D212—22no—
353D212—22no—
354D212—48no—
355D212—42no—
356C4×D53—24no—
357C4×D53—22no—
358C4×D53—22no—
359C4×D53—48no—
360C8×C53—22no—
361C8×C53—22no—
362#88322—22no—
363#88322—22no—
364C2×#3317—531nomaximal, Sylow
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—44no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—84no—
373C22×C53#54612yes—
374C22×C53#57512yes—
375C22×C53#57712yes—
376C22×C53C23×D411yescharacteristic
377C2×D53—22no—
378C2×D53—22no—
379C2×D53—22no—
380C2×D53—44no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—84no—
385C4×C53—24no—
386C4×C53—22no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53#54612yes—
390C4×C53C22×#4111yescharacteristic
391C4×C53C2×H(5,𝔽2)11yescharacteristic
392Dic53—22no—
393Dic53—22no—
394Dic53—22no—
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×#552—531no—
399C2×#550—531no—
400#3317—5316no—
401C2×#490—531no—
402C2×#481—531no—
403C2×#482—531no—
404C2×#479—531no—
405C2×#468—531no—
406C2×#465—531no—
407C2×#460—531no—
408C2×#452—531no—
409C2×#452D5311yescharacteristic, complemented
410C2×#441—531no—
411C2×#435—531no—
412C2×#417—531no—
413C2×#416—531no—
414C2×C53—42no—
415C2×C53—82no—
416C2×C53#331714yescomplemented
417C2×C53C2×#54611yescharacteristic
418C2×C53C2×#57511yescharacteristic
419C2×C53C2×#57711yescharacteristic
420D53—42no—
421D53—82no—
422C22×#41—531no—
423C22×#41C2×D5311yescharacteristic
424C22×Q16C2×D5311yescharacteristic
425C22×SD16—531no—
426C22×SD16C2×D5311yescharacteristic
427C22×M16—531no—
428C23×C8—531no—
429#552—538no—
430#552—1064no—
431#550—538no—
432#550—1064no—
433C2×#127—531no—
434C2×#127—1061no—
435C2×#126—1061no—
436C2×#125—531no—
437C2×#125—1061no—
438C2×#123—1061no—
439C2×C22⋊Q8—531no—
440C2×C22⋊Q8C2×D5311yescharacteristic
441C2×#121—531no—
442C2×#121—531no—
443C2×#121—1061no—
444C2×#121—1061no—
445C2×C4×Q8—531no—
446C2×C4×Q8—531no—
447C2×C4×D4—531no—
448C2×C4×D4—1061no—
449C2×#117—531no—
450C2×#117—1061no—
451C22×C4⋊C4—531no—
452#490—538no—
453#482—538no—
454#481—538no—
455#479—538no—
456#468—538no—
457#465—538no—
458#460—538no—
459#452—538no—
460#452C2×D5318yescomplemented
461#441—538no—
462#435—538no—
463C2×#107—531no—
464C2×#106—531no—
465C2×#106—531no—
466C2×C4⋊C8—531no—
467#417—538no—
468#416—538no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103C2×D5311yescharacteristic
473C2×#102—531no—
474C2×#102—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102C2×D5311yescharacteristic
479C2×C22⋊C8—531no—
480C2×C22⋊C8C2×D5311yescharacteristic
481C2×#97—531no—
482C53C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41—534no—
487C2×#41—1062no—
488C2×#41—1064no—
489C2×#41—2122no—
490C2×#41C22×D5314yes—
491C22×Q8C22×D5311yescharacteristic
492C22×Q8C22×D5311yescharacteristic
493C22×D4—21no—
494C22×D4—531no—
495C22×D4—531no—
496C22×D4—1061no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4—1061no—
501C22×D4C22×D5311yescharacteristic
502C23×C4—21no—
503C23×C4—531no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4C22×D5311yescharacteristic
507C2×Q16—24no—
508C2×Q16C22×D5314yes—
509C2×SD16—42no—
510C2×SD16—534no—
511C2×SD16—2122no—
512C2×SD16C22×D5314yes—
513C2×M16—534no—
514C2×M16—2122no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—534no—
518C22×C8—2122no—
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5311yescharacteristic
521#127—534no—
522#127—1062no—
523#127—1068no—
524#126—1068no—
525#125—534no—
526#125—1062no—
527#125—1068no—
528#123—1068no—
529C22⋊Q8—22no—
530C22⋊Q8—534no—
531C22⋊Q8—1062no—
532C22⋊Q8C22×D5314yes—
533#121—534no—
534#121—534no—
535#121—1068no—
536#121—1068no—
537#121—1062no—
538#121—1062no—
539C4×Q8—534no—
540C4×Q8—534no—
541C4×Q8—1062no—
542C4×Q8—1062no—
543C4×D4—534no—
544C4×D4—534no—
545C4×D4—1068no—
546#117—534no—
547#117—1068no—
548#117—1062no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—534no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1062no—
562C2×C4⋊C4C22×D5311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—531no—
565C2×C22⋊C4—531no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C42—531no—
571C2×C42—1061no—
572C2×C42—1061no—
573C2×C42—1061no—
574#107—534no—
575#106—534no—
576#106—534no—
577C4⋊C8—534no—
578#103—534no—
579#103—534no—
580#103—534no—
581#103C22×D5314yes—
582#102—534no—
583#102—534no—
584#102—534no—
585#102—534no—
586#102—534no—
587#102C22×D5314yes—
588C22⋊C8—534no—
589C22⋊C8C22×D5314yes—
590#97—534no—
591C24—21no—
592C24—531no—
593C24—1061no—
594C24D4×D5311yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598#41—1068no—
599#41—2124no—
600#41—2128no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8#1171994714yes—
607C2×Q8C23×D5312yes—
608C2×Q8C23×D5312yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—44no—
614C2×D4—534no—
615C2×D4—532no—
616C2×D4—1064no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1064no—
621C2×D4—1061no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—4242no—
625C2×D4—4242no—
626C2×D4—4242no—
627C2×D4—2124no—
628C2×D4—2122no—
629C2×D4—2124no—
630C2×D4C23×D5312yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—531no—
639C22×C4—531no—
640C22×C4—531no—
641C22×C4—532no—
642C22×C4—532no—
643C22×C4—1064no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1064no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4D4×D5312yes—
653C22×C4D4×D5311yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—28no—
657SD16—44no—
658SD16—2124no—
659M16—2124no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—2124no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—534no—
672C4⋊C4—532no—
673C4⋊C4—532no—
674C4⋊C4—532no—
675C4⋊C4—1064no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1061no—
681C4⋊C4—1061no—
682C4⋊C4—1064no—
683C4⋊C4—1061no—
684C4⋊C4C23×D5312yes—
685C22⋊C4—24no—
686C22⋊C4—534no—
687C22⋊C4—534no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C42—532no—
693C42—532no—
694C42—1064no—
695C42—1064no—
696C42—1064no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—532no—
705C23—1062no—
706C23—1062no—
707C23—1062no—
708C23—1062no—
709C23—2122no—
710C23—2122no—
711C23—2122no—
712C23C2×D4×D5312yes—
713C23C2×D4×D5311yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—22no—
717Q8—22no—
718Q8—42no—
719Q8C2×#1171994714yes—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—42no—
724D4—1062no—
725D4—1062no—
726D4—4244no—
727D4—4244no—
728D4—4244no—
729D4—2128no—
730D4—2124no—
731D4—2128no—
732D4—2122no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—532no—
745C2×C4—532no—
746C2×C4—532no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1064no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—2128no—
757C2×C4—2128no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4C2×D4×D5312yes—
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4C2×#1171994712yes—
764C2×C4#1313326212yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1062no—
769C8—1062no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—84no—
778C22—1062no—
779C22—1062no—
780C22—1062no—
781C22—4244no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22—2124no—
786C22#1681126012yes—
787C22#1681142212yes—
788C22#1681143012yes—
789C22C22×D4×D5311yescharacteristic
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—1062no—
795C4—1062no—
796C4—1062no—
797C4—2122no—
798C4—2122no—
799C4—2122no—
800C4#1681126012yes—
801C4C22×#1171994711yescharacteristic
802C4C2×#1313326211yescharacteristic
803C2—42no—
804C2—82no—
805C2—4242no—
806C2—2122no—
807C2#2028683414yesdirect product factor
808C2C2×#1681126011yescharacteristic
809C2C2×#1681142211yescharacteristic
810C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC2×#16811292C2
hypercenterC2×#452D53
hypocenterC53C2×#3317
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16811315C2semidirect
3. #20286834C2direct (N × H)
4. C2×#16810986C2semidirect
5. C2×#16810942C2semidirect
6. C2×#16810946C2semidirect
7. C2×#16810928C2semidirect
8. C2×#16810871C2semidirect
9. C2×#16810849C2semidirect
10. C2×#16810821C2semidirect
11. C2×#16810784C2semidirect
12. C2×#16810730C2semidirect
13. C2×#16810697C2semidirect
14. C2×#16810624C2semidirect
15. C2×#16810618C2semidirect
16. C2×C53×#452C2semidirect
22. #16811315C22semidirect
43. #16810986C22semidirect
44. #16810946C22semidirect
45. #16810942C22semidirect
46. #16810928C22semidirect
47. #16810871C22semidirect
48. #16810849C22semidirect
49. #16810821C22semidirect
50. #16810784C22semidirect
51. #16810730C22semidirect
52. #16810697C22semidirect
57. #16810624C22semidirect
58. #16810618C22semidirect
73. C53×#452C22semidirect
409. C2×#452D53semidirect
416. C2×C53#3317semidirect
460. #452C2×D53semidirect
482. C53C2×#3317semidirect
807. C2#20286834direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168113152
C2×#168112922
#202868342
C2×#168109862
C2×#168109422
C2×#168109462
C2×#168109282
C2×#168108712
C2×#168108492
C2×#168108212
C2×#168107842
C2×#168107302
C2×#168106972
C2×#168106242
C2×#168106182
C2×C53×#4522
C2×#331753